Optical phase angle measuring apparatus



Dec. 8, 1964 H. GAMO OPTICAL PHASE ANGLE MEASURING APPARATUS Filed Dec.30, 1960 7 Sheets-Sheet 1 CORRELATOR 5 fi B. 'w DETECTOR i I l OUTPUT d1 MULTIPLIER |NTEsRATOR-\-- LIGHT BEAM 2 DETECTOR l a |2 LIGHT BEAMPHOTO DETECTOR H COHERENT VARIABLE J eAcxsnouuu- PHASE d CORRELATOROUTPUT SOURCE BEAM SHIFTER e o I I52 LIGHT BEAM 2 PHOTO J"'DETECTOR l7FR M TUNED QUARTER Low FREQ. A E MPLIFI R 34 SQUARE AMPLIFIER mTEeRAToRMUlIIPLIER 0 3 u INVENTOR.

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OPTICAL PHASE ANGLE MEASURING APPARATUS Filed Dec. 30, 1960 '7Sheets-Sheet 6 FIG.7

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I47 5 5 PHASE I A (I +COSmH SHIFT I FIGJO United States Patent 3,160,696OPTICAL PHASE ANGLE MEASURING APPARATUS Hideya Gamo, Katonah, N.Y.,assignor to International Business Machines Corporation, New York, N.Y.,a corporation of New York Filed Dec. 30, 1960, Ser. No. 79,370 19Claims. (Cl. 88-14) the times of emission of photoelectrons at differentpoints illuminated by coherent beams of light are partially correlated.The authors state that this result forms a basis for the claim that thecorrelation is essentially an interference effect exemplifying the wave,rather than corpuscular, aspect of light. The intensity interferometertherefore is quite important in modern physical optics, since itdevelops a correlation function for the intensity fluctuations in twocoherent, or partially coherent, beams of light by sampling the currentsfrom two photodetectors upon which said beams impinge.

The correlation function derived by the original Hanbury Brown and Twissinterferometer is proportional to the square of the absolute value ofthe phase coherence factor of the two beams. The phase coherence factoritself is a complex number having a phase as well as an absolute value.As will subsequently be pointed out, knowledge of this phase isdesirable for certain measurements. However, such phase informationcannot be conveniently ascertained from merely the square of theabsolute value of the phase coherence factor.

It is therefore an object of the present invention to provide anintensity interferometer with a source of coherent background so thatcomplete information about the phase coherence factor may be determined,including its phase.

Another object of the present invention is to provide means to measurethe magnitude and phase of the phase coherence factor for any timedelay.

Another object of the present invention is to provide a coherentbackground source for the direct measurement of the cross-spectraldensity of the incident beams.

These and other objects of the invention will become apparent during thecourse of the following description, when taken in conjunction with thedrawings, in which:

FIGURE 1 shows the prior art intensity interferometer;

FIGURE 2 shows a block diagram of the present invention with coherentbackground;

FIGURE 3 shows one embodiment of the present invention using coherentbackground for measuring the phase coherence factor;

FIGURE 3:: shows an electronic synchronous detector for use in FIGURE 3;

FIGURE 4 shows a slightly difierent embodiment from that in FIGURE 2;

FIGURE 5 shows another embodiment of the present invention wherein theincident beams are delayed;

FIGURE 6 shows a slightly different embodiment than FIGURE 5;

FIGURE 7 shows one form of a multiplier for use in FIGURE 6;

"ice

FIGURE 8 shows a slightly difierent embodiment from that in FIGURE 7;

FIGURE 9 shows another embodiment of the present invention usingcoherent background for the measurement of cross-spectral density; and

FIGURE 10 shows .a slightly dififerent embodiment from that in FIGURE 9for the measurement of crossspectral density.

In order to fully appreciate the novel concepts of the presentinvention, reference will first be made to the intensity interferometeroriginally proposed by authors Hanbury-Brown and Twiss in publications Aand B identified above. FIGURE 1 shows a simplified block diagram ofthis prior art device. Fully or partially coherent quasi-monochromaticlight beams 1 and 2 are respectively incident on the two photodetectors3 and 4, the output currents of which are proportional to theinstantaneous intensity of light I (t) and 1 (2) and are directed to thecorrelator unit 5. In correlator 5, a multiplier 6 takes the product ofthe two currents which is then integrated with respect to time byintegrator 7. The output from the integrator 7 is a measure of the crosscorrelation existing between the photon distributions in the light beams1 and 2. Photodetectors 3 and 4 may have time constants greater than thecoherence time of the incident beams, which is usually on the order of 3X 10- seconds. Multiplier 6 can be any one of many well known analogmultipliers, while integrator 7 is shown by Hanbury- Brown and Twiss tobe a motor having a linear relation ship between speed and inputvoltage. Of course, any purely electronic integrating circuit may alsobe used.

According to the theory of Hanbury-Brown, Twiss, and others, thecorrelation coeflicient between the light beams is given by thefollowing formula:

where M AI is the correlation coefficient, 1' is the coherence time oflight, T is the response time of the detector, I and I are the averagevalues of light intensity at the inputs of the photodetectors 3 and 4-,and 712 is the complex degree of coherence or normalized mutualcoherence factor, for the light beams as measured between two points Aand B, physically spaced d distance apart, whereat detectors 3 and 4 arelocated. The symbols surrounding the values I and 1 indicate that theintegral with respect to time (usually, the observation time) is takenof the instantaneous light beam intensities at the respectivephotodetectors in order to obtain their time average, i.e., j l (t)a't=l and The fluctuations (or A.C. Values) of the light beam intensitiesare given by AI l I and and A1 are represented by the output currentsfrom photodetectors 3 and 4, respectively, which are proportionalthereto. Therefore, after multiplication and integration with respect totime, the output from integrator 7 is AI AI which, as defined above, isa measure of the correlation coetficient.

According to Principles of Optics, Born and Wolf, Pergamon Press (1959),page 504 (hereinafter referred to as Publication C), the complex degreeof coherence 712 for quasimonochromatic light is defined to be the timeaverage of the product of the wave amplitude of light at point A(FIGURE 1) and the complex conjugate of the 3 wave amplitude of point B,divided by the product of the square roots of the intensities at thesepoints. Thus,

where V (t) =wave amplitude of light at point A, V *(t)=complexconjugate of wave amplitude of light at point B, and Z and I=intensitiesof light at points A and B, respectviely. 'y is also termedthe phase coherence factor and it is a complex number having both realand imaginary parts. In polar coordinate form, therefore, 712 may berepresented as ['y |(c os +i sin qb), or |'y [e where is theabsolutevalue of 7 and is equal to the square root of the sum of the squares ofthe X and Y vectors, while is the phase angle that makes with the Xaxis. Physically, the angle may be defined geometrically as on page 508of Publication C, which is herein incorporated by reference. For fullycoherent light beams at points A and B, [=l, while for fully incoherentlight beams, ]=0. Therefore, for partially coherent light beams, O |'yl.

One other important aspect of the phase coherence factor 712 should bementioned here in order to later appreciate the distinction between theseveral species of the present invention. This factor, as defined aboveand as measured by Hanbury-Brown and Twiss, is derived by consideringthe light wave amplitude Vibrations at points 7 A and B at the sameinstant of time; hence, the terms V (t) and V *(t) are employed inderiving Formula 2 and indicate that there is no difference between thetimes of arrival of corresponding portions of the two incident waves attheir respective sampling points. However, if the vibrations at point Bare considered at time 7- later than those at point A (or vice versa),then wave amplitudes V (t+'r) and V *(z) must be used in deriving thephase coherence factor. In order to distinguish between the cases where7:0 and 7;:0, the term 7 (7) will be henceforth used for the latter. Aswill subsequently be explained, determination of the phase angle 11: ofa factor 'y ('r), where n+0, is important in the event that the crossspectral density of the incident light beams is desired. However,certain modifications to the intensity interferometer may be requireddue to the fact that the coherence time of light is extremely short.

It is therefore seen that while the original Hanbury- Brown and Twissinterferometer of FIGURE 1 provides a measure of the absolute value of'y (since the c0rrelation coeflicient observed is proportional to 17121the phase of the phase coherence factor cannot be convenientlyascertained. Also, the shot noise in the optical region of thephotodetectors, due to photoelectrons, is predominant over the waveinteraction noise, so that all noise in the intensity interferometer ofFIGURE 1 can be ap proximated by 'this shot noise which is given byTherefore, the signal to noise ratio of FIGURE 1 is proportional to iizi'nzi v n z Because for partially coherent light is less than 1, thesquaring of l'y l results in a fairly low S/N figure.

Because of the reasons stated previously, the phase of the complexdegree of coherence yields valuable information, especially whendetermining intensity distribution of a source or the phase of anilluminated object. An intensity interferometer measuring both phase andamplitude of the factor 'y is the subject of the present invention,which provides a coherent background source for the interferometer ofHanbury-Brown and Twiss. This novel feature is generally shown in blockform in FIG- URE 2. A beam of light 15 generated from a coherent source10 is supplied to bothinput channels of the original Hanbury-Brown andTwiss interferometer as composed of photodetectors 12, 13, andcorrelator 14. Beam 15 is first divided into two separate beams 15 and15 by a phase shifter 11 so that a phase difierence of 0 existstherebetween. The value of 6 may be varied in a manner subsequently tobe explained. Each beam 15 and 15 should have the same intensity I Beam15 is then combined with beam 1 (having intensity I at mixer 8 with thereesultant beam 16 (having intensity I +I being incident uponphotodetector 12. In like fashion, beam 15 is combined with beam 2(having intensity I at mixer 9 with the resultant beam 17 (havingintensity I +I incident on photodetector 13. The coherent lightbackground 10 should preferably be a stable monochromatic point sourcewhose intensity is as high or higher than the incoming beams 1 and 2. Inpractice this coherent background may be provided by a mercury (Hg) 198lamp commercially available having a spectrum of approximately 5461 A.The best source for this purpose would actually be a continuous waveoptical maser.

The basic principle of operation of the modified interferometer ofFIGURE 2 is the same as that shown in FIGURE 1, in that the crosscorrelation coefiicient is taken of the two photodetector currents,which in turn are proportional to the intensities of the beams 16 and17. Thus, the observed correlation becomes in this case where 1' 0+ 1I2, I0+I2 1 2' is the correlation coefiicient, and is the phasecoherence factor.

The relation between the coherence factor 7 of FIG- URE 2 and the factor712 of FIGURE 1 may be derived in the following manner. Since then v12'=1' 2'* 1' 2' where V '=wave amplitude of light beam 16 at point A, and V*=complex conjugate of the wave amplitude of light beam 17 at point B.The magnitude of the wave amplitude V is attributable to the sum of thewave amplitude V of beam 2 and of the wave amplitude of beam 15 whichcan be represented by V In like fashion, V is the sum of V (waveamplitude of beam 1) and of the wave amplitude of beam 15 which isrepresented by V e where 0 is the phase difference between beams 15 and15 Thus,

V '=V +V e 2'= 2+ o (7) Substituting Equations 6 and 7 into Equation 5,We

I have Equation 1 thereby shows the relationship between of FIGURE 2 and712 of FIGURE 1. 7 is the phase coherence factor of the incident beams 1and 2 under consideration, and may be expressed in polar coordinate formas ]e It should be appreciated in Equation 10 above that both 712 and 'yrefer to the case where there is no time delay (1-=0) in considering thewave vibrations at the two photodetectors. The purpose of the intensityinterferometer in FIG- URE 2 is to enable the measurement of angle 4: aswell as l'yml.

To see how this is done, consider the expansion of Equation 4 whendefining according to Equation 10.

Since the square of the absolute value of a complex number is equal tothe product of that number and its complex conjugate,

In Equation 11, the third term may be reduced as follows:

Since 2 cos a+i sin a, the right-hand term of Equation 12 becomes=!*/12| sin Sin (Hon i'Y12l C05 fi) l'Yiz -iel where the superscript Rsignifies that only the real term of the expanded bracketed value needbe considered.

Thus, Equation 11 becomes From Equation 14 it may be understood thatvariation in the correlation coefficient, as represented by AI 'A1 fromthe output of the correlator in FIG- URE 2, depends only upon the phaseangle 0 of the optical phases shifter 11, since it can be assumed thatthe values I I HM, and 1 remain constant. Therefore, the maximum outputsignal from the correlator is obtained when the phase 0 of phasecoherence factor 712 is cancelled by the phase diiference 9 in thecoherent background applied to the two input channels. This is so,because when 0=O, cos(6)=1. The minimum output is similarly obtainedWhen 9:1r' or an odd member multiple of Ir, since cos 7r=1. In the firstof these cases, therefore, the term 2I \/I I ]'y I is added to the othertwo terms in Equation 14, while the minimum signal case results in thisterm being subtracted therefrom.

A simple procedure for measuring the phase angle 5 of the phasecoherence factor 712 may be derived following the teachings above. Byvarying the angle 0, by any one of a number of well known ways, theoutput from correlator 14 may be maximized, at which time 0 will equalThe absolute value of may be ascertained by varying 6 until the outputis minimized, then apply the formula (Max-Min) 2. Another way is bymerely discontinuing the use of the coherent background so that thecorrelator output equals I I as in FIG- URE 1.

Concerning the signal to noise ratio S/N of the intensity interferometerwith coherent background, the

6 term appears in Equation 14, and the signal is proportional toIQVEI'YHI. The noise is proportional to v1.7; which equals 1,+1 1 +1Since I, is substantially higher than I or I D+ 1) o-P 9 0 Therefore,the S/N of FIGURE 2 is proportional to Comparing Equation 15 withEquation 3, it is seen that the S/N of FIGURE 2 varies according to [vinstead of l'y as in FIGURE 1. Since the phase coherence factor l'ylglis generally less than unity, this fact may be significant, especiallywhere is small.

FIGURE 3 shows a practical embodiment of the intensity interferometerwith coherent background used for measuring the absolute value of i'y land its phase 5. Light beam 1 is introduced via a focusing lens 18 to ahalf-silvered mirror 19 which transmits beam 1 with little or noattenuation to phototube 20. In like manner, beam 2 is passed via lens21 and half-silvered mirror 22 to phototube 23. The background sourceprovides a coherent beam 24 which is collimated when passing throughlens 25 to half-silvered mirror 26 positioned so that half of the beam24 intensity is reflected downward as beam 24 to strike mirror 22, Whilethe remainder of beam 24 passes through mirror 26 to strike mirror 27.The reflected beam from mirror 27 returns to mirror 26 and is reflectedup as beam 24 to strike mirror 19. Beams 24 and 24 are respectivelyreflected at mirrors 19 and 22 to combine with beams 1 and 2 to formbeams 28 and 29.

A variable phase angle 0 between beams 24 and 24 may be obtained bymoving mirror 27 in a direction Ax so that the distance x changes. Thus,

Where is the wavelength of the coherent background light. Althoughmirror 27 can conceivably be moved and set to any value of 0, the exactmeasurement of 0 may be difficult due to the extremely small values ofAx and A. A more practical scheme is that shown in FIG- URE 3.Stationary mirror 202 is provided to reflect back a portion of beam 24to mirror 26 and thence to mirror 293. Also, a portion of beam 24 as itreturns from movable mirror 27, passes through mirror 26 to strikemirror 203. These two beams are reflected from mirror 203 up to aphotodetector 31. A means 30 slowly moves mirror 27 continuously in thesame direction Ax for the duration of observation. The continuous changein phase of beam 24 with respect to beam 24 causes an interferenceeffect at photodetector 31 which, via tuned amplifier 37 generates a lowfrequency signal A (1+ cos wt), where wt: 0, and w=2dx/dt such thatangle 0 is modulated with respect to time. The purpose of thismodulation of 0 will subsequently be explained.

The current outputs from phototubes 241 and 23, which are proportionalto the intensities I and 1 of beams 28 and 29, respectively, are fed toa multiplier 34. Amplification of these currents may first be requiredin ampli fiers 32 and 33, which can also be provided by usingphotomultipliers having amplification due to secondary emission ofelectrons. The output current from multiplier 34 is applied aftersuitable amplification by tuned amplifier 34 to one Winding of two-phasemotor 35. The input to the other Winding of motor 35 is taken from theoutput of a variable phase shifter 36 which is used to vary the phase ofthe low frequency signal A(1+cos wt) from photodetector 31 by an amount[1. Thus, the output from phase shifter 36 is A [1+cos (wt-H0) A counteror other such device 37 may be used to measure the total number ofrevolutions during the observation time, or the rpm.

flected and is introduced into the same lens 43 7' In operation, themultiplier 34 in FIGURE 3 provides an output according to Equation 14wherein the third term becomes 2I /I I ]'y [COS (wt- 5), since 0=wt.Because the first and second terms in this Equation 14 are clearlyconstant, the quantitities corresponding to these terms will vanishafter integration by the motor, so that only the third term contributesto any net rotation thereof. Since the output from phase shifter 36 is acurrent proportional to A[1+cos (wt-hid], it is observed that the termwt in both inputs to motor 35 will cancel, so that the torque isproportional to cos where qb is the phase angle of the phase coherencefactor 40 Therefore, by observing the maximum degree of motor rotation,which occurs when cos (r,'/)=l, the angle can be determined by notingthe value of 1,0. The advantage of measuring phase \l/ instead of phase0 is that the former is easily obtained from any well known calibratedelectronic phase shifter 36 which operates on low frequency electricsignals.

Instead of using the two-phase integrating motor 35, the same proceduremay also be realized by a synchronous detector and integrating network,where the signal from multiplier 34 is detected under the presence ofthe signal phase shifter 35. Such a circuit is shown in FIGURE 3a, andmay include a quarter square multiplier 2053 such as is shown anddescribed on page 281 of Electronic Analog Computers, Korn and Korn,McGraw-Hill Publishing Co. (2d Ed.) 1956. This multiplier is responsiveto the outputs from amplifier 34 and phase shifter 36 in FIGURE 3 togenerate a signal proportional to their product, which in effect is thefunction also of motor 35. In order to eliminate higher order harmonicsin this output, amplifier 291 may be provided having an upper cutolifrequency less than the value to. The output therefrom is then appliedto some form of integrator 292, such as the well known capacitor type,for generating the final output signal over the observing time interval.

In the event that the maximum distance Ax in FIG- URE 3 is traversedbefore significant output results are obtained from the intensityinterferometer, the direction of motion of mirror 27 may be reversed ifthe phase 1/ of shifter 36 is likewise changed in polarity. Using thisprocedure, the observation time may be extended indefinitely until avalid measurement is made.

FIGURE 4 shows intensity interferometer similar to that in FIGURE 3,except for a modification in the optical front end wherein the phase ofthe coherent background light is varied. The incident beams 1 and 2 tobe analyzed are derived from an extended source so that they travelthrough a half-silvered mirror 38 on their way to phototubes 39 and 4%,respectively. The coherent background source 49 is located so that itsrays 41 and 42 reflect off of mirror 38 to become incident onphototu'oes 3? and 40. Mirror 38 and distance R should be such that themirror image of coherent source 49 should coincide with the center ofthe extended incident source of incident waves. By moving the coherentbackground source in a direction d, a phase difference 0 between thecoherent background beams 42 and 4-1 is created at photodetectors 39 and40.

The low frequency signal corresponding to varying phase difference 0between the background beams is produced by a system similar to theMichelson stellar interferometer. Namely, the light beam 41 is reflectedby a semi-transparent mirror 39 and is again reflected and introducedinto a lens 43 The other beam 42 is re- The above two beams aresuperposed at the third photoelectric detector 44 by the above lens andproduce interference pattern between the abovementioned beams. Theoutput signal from photodetector 44 is given by A l +cos wt)- whensource 49 is moved by means 48 The interference between light beams fromthe extended source of object,

which is assumed as not moving, should be constant. The output ofphotodetector due to the object source is easily eliminated by means oftuned amplifier 47 Using the parameters R R d, and r in FIGURE 4, it maybe easily shown that 0 (the phase difference between coherent beams 41and 4-2 at photodetectors 39 and 44)) is approximately equal to where Ais the wavelength of the coherent background, and the value of r issmall compared to that of /R +12 In FIGURE 4, the remainder of theinterferometer to the right of the photodetectors is the same as shownin FIGURE 3, the operation of which has already been described.

Turning to FIGURES 5 and 6, further embodiments of the present inventionwill be described. As has already been explained, the discussion givenin connection with FIGURES 1, 2, and 3 is limited to the case where 7:0,i.e., where corresponding portions of the light vibrations areconsidered at the same time. An extension of this technique alsoprovides for the measurement of a (1'), where TS O. This quantity is ofparticular importance where it is desired to calculate the crossspectral density G (V) of the amplitude fluctuations of incident beams land 2 according to the following formula where V is the frequency underexamination, while (7) and 1- are as defined above. The function G (V)represents the amplitude correlation between points one and two atfrequency V and is the optical analog of the concept of cross-powerspectrum in the theory of station ary random processes. Equation 16shows that the functions 0-) and G (V) form a Fourier transform pair.Since 'y r) ='Y12" (-r) (using the analytic signal form as described byPrinciples of Optics, pages 493 et seq.), and 'Y12(T):I'Y12(T) laEquation 16 becomes From Equation 17, it is seen that the spectrum islimited to the positive frequency. Therefore, the amplitude of anyfrequency component present in the interfering light beams may bemathematically calculated provided that the value of (1) is known forall values of 7 having the range 056m. A simplified formula forcalculating G12(V), using only certain specific values of willsubsequently be developed.

It should be appreciated that the value of (1) used in the abovecalculations includes both its real and imaginary parts, thus callingfor the measurement of its phase as as well as absolute magnitude. Thismeasurement may be made by the apparatus in either FIGURE 5 or FIG- URE6. Newly added mirrors 53, 54, and 55 in FIGURE 5 are provided to changethe optical path length of the incident beam 2, so as to introduce atime delay 7' into this beam at photodetector 57 when compared with theincident beam 1 at photodetector 52. Incident beam 2 is directed througha half-silvered mirror 53 to be reflected back thereto from mirror 54.The reflected beam 2 then is reflected from mirror 53 to mirror 55 andthence to be combined with the coherent beam at mirror 56. Mirror 54 maybe moved to any position Ay so as to vary the optical path traversed bybeam 1 in reaching photodetector 57. When using the coherent backgroundfor measuring the phase angle 6 of (7), the operation of FIGURE 5 may bedescribed as in Equations 4, 10, and 14, except that the term (7)appears, instead of 7 (indicating that 7:0).

Thus,

Equation 18 should be compared with Equation 14. As with FIGURE 3, anyvariation in the correlation coefiicient for a particular value of '1'when using coherent background, is due to a change in the phase angle 0.Thus, when cancels the phase angle 5 of 7 (7), maximum output isobtained. Mirrors 58 and 67, together with photodetector 62 and phaseshifter 65, may be provided in FIGURE 5 as was done in FIGURE 3 so thatthe 0 components applied to the two-phase motor 64 will cancel, leavingthe phase it as the observable parameter when the output is maximum.

FIGURE 6 shows a device similar to that of FIGURE 5 for the measurementof (7), using coherent background, where the delay 1' is performed onone of the photodetector currents before it reaches the multiplier.Theoretically, the insertion into the original I-Ianbury- Brown andTwiss interferometer of a delay '7' (unit 82) between the output of onephotodetector 75 and the multiplier 83, such as is shown in FIGURE 6,results in the measured correlation function being proportional to thesquare of the absolute value of (7) according to the following formula:

since the output currents from the photodetectors are pro portional tothe respective light beam intensities so that a delay (1-) of thecurrent in one of said channels before reaching the multiplier isequivalent to considering the light vibrations at said channel at a time(1-) later than those at the other channel. Now, by superimposing themonochromatic and coherent background onto the incident beams at thephotodetectors, such as is done in FIGURE 6, the measuredcross-correlation function becomes 1'( 2'( -l- =|"/1z'( 1' 2' where theabove quantities are defined as in Equation 4. The relation between 'y'(1-) of Equation 20 and (7) of Equation 19 may be derived in the samemanner as set forth by Equations 5, 6, 7, 8, and 9, keeping in mind thatthe total phase difference between the split beams of coherentbackground is now equal to 6+w -r, where 6' is the change in phase dueto the phase shifter 79, and w r is the change in phase due to the delay82, where w is 2 7r times the frequency of the coherent light. lThus,

we)=wfilmm+roe llv n+ln(1H0) Equation 21 should be compared withEquation 10,

the latter being developed while considering that 7:0,

It can be seen from Equation 22 that the output from the correlator ismaximum for any set value of '7", when the phase of 'y (1-) cancels thephase w T+t9, or when (w T+t9)=21r1 With 17:0,1 Since both (00' 1-, and0 may be determined by conventional means, the value of for any '1', maylikewise be determined according to the principles hereinbeforedescribed, as well as the absolute value of FIGURE 6 also incorporatesmotor means 79 for moving mirror 7 S in a manner previously described,together with means 76, 81, and 89 for developing a signal A(l+cos wt).Phase shifter 86 provides a shift of 1, the value of which is equal to 0for purposes of providing maximum rotation of motor 84.

In order to successfully measure (1) by the apparatus shown in FIGURE 5or in FIGURE 6, an important requirement is that the photodetectorstogether with multiplier must have a response time T that is muchsmaller than the coherence time T of the light incident on thephotodetectors. The average coherence time for light under considerationis approximately 3 l0- seconds. If the response times (or timeconstants) of the abovementioned components are larger than thiscoherence time, the correlation function Al (t)Al (t-|-'r) be comesindependent of 1-. Thus, high speed components 52, 57, 63, and 72, 75,83 are essential in FIGURE 5 and FIGURE 6, respectively. Photomultipliertubes commercially available may not satisfy this requirement sincetheir time constants are, for practical purposes, limited by the spreadin transit time through the multiple amplification stages due to thesecondary electron emission. However, the delay in the photoelectronemission process, itself, is much less than 10* seconds, as wasexperimen tally shown by Forrester et al. Physical Review, vol. 99, page1691 (1955). This phenomenon may be used in developing a high speed unitfor carrying out the functions of FIGURE 5 and FIGURE 6.

When the phase difierence 0 is cyclically modulated such that 0=wl, thenthe physical details of blocks 68 and in FIGURES 5 and 6, respectively,may assume the following form. Each photoelectron emitted from thecathode of a photodetector is collected by its anode to which is coupleda coaxial transmission line C1 or C2. The transfer of a photoelectronfrom cathode to anode generates an electromagnetic wave front whichpropagates down the line at the light speed. The coaxial lines may bediagrammatically represented as in FIGURE 7, which is an alternativeform of high speed multiplier than, the one presently being explained.The multiplying circuit in FIGURES 5 and 6 may consist of asemiconductor diode (such as R7 in FIGURE 7), acting as a square lawdetector. Such diodes have an extremely fast response time, and, whenused in their non-linear region, can perform a squaring operation on theabsolute value of an input signal thereto as is well known in the art.The two signals 1 and I from the photodetectors are therefore firstsummed together, then applied to the diode for squaring, as may be seenin the multiplying circuit of FIGURE 7. The output from the multiplieris then applied to amplifiers 63 and 84 (FIGURE 5 or 6) which is tunedto extract signals having the frequency characteristic to,

which is the modulation frequency of the coherent phase difference 0.This tuned amplifier has a time response much larger than the coherencetime of the light.

The operation of the above-described circuit is as follows: For the sakeof simplifying the following analysis, assume that 7:0. Let V 0) and V0) ==the wave amplitudes of the incident beam 1 and coherent beam,respectively, at the channel 1 photodetector, and V (t) and V 0) :theWave amplitudes of the incident beam 2 and coherent beam, respectively,at the channel 2 photodetector. As previously noted in connection withEquations 6 and 7, V (t)=V (t)e The resultant wave amplitude at thefirst and second photodetectors, respectively, is therefore V (t){-V(t), and V (t)|V (t). Hereafter, the independent variable (t) will beomitted from the equations.

Since the currents I and I represent intensity which is equal to thesquare of the absolute value of wave amplitude, then 1'=1I 1+ 1ol z'= 2lz+ zo[ where a; and or; are photodetector parameters. Summing together1; and I then applying this sum to the diode square law detector, theoutput therefrom assumes the following form when neglecting parameters aand a 1 1 Because of the extremely high frequencies of the first andsecond terms in Equation 25, only the third term need be analyzed. Whenthis term is expanded, and its high frequency terms eliminated (becauseof tuned amplifier 63 or 84), then the resulting output from block 68 oris V2*V1V10* V20+V1V2$ V oVgo Since the tuned amplifier performs anintegration function with respect to the V and V signals (because of itsslow response time, then the output may be represented as Since V V =I(unnormalized phase coherence factor), V1V2 =r 12, V10 'V2 and V10V2g*l3 then the output from the tuned amplifier as the time response thereofapproaches is [F le Thus, the high speed components described aboveperform correlation on the photodetector outputs, and may be used evenwhen 7720.

In the event that angle 9 is not modulated according to wt, but insteadis adjusted manually or otherwise, a slightly difierent high speedmultiplier must be used. In FIG URE 7 are shown details of such a highspeed unit which may be substituted for the contents of the dot-dashblock 68 in FIGURE 5 and the dot-dash block 99 in FIGURE 6 when thephase shifter it and a synchronous detector are not used. The superposedincident beams and coherent beams for each channel are applied tophotodetectors 94 and 99 via low frequency light choppers 93 and 98,respectively. Light choppers 93 and 98 modulate the amplitudes of theincident light waves thereon at frequencies of m and m respectively.They may take any one of several well known forms, such as a rotatingsector or the like. After leaving the light choppers, the respectivebeams impinge upon the cathodes of detectors 94 and 99, causingphotoelectron emission having a time constant less than l0- seconds, asdiscovered by Forrester et al. Each photoelectron emitted from thecathode is collected by the anode to which is coupled a coaxialtransmission line. The transfer of a photoelectron from cathode to anodegenerates an electromagnetic ,wave front which propagates down thecoaxial line at the light speed.

At photodetector 94, line 96 is connected to the anode, together with aresistor 95 which should be matched with the characteristic impedance ofthe line for maximum energy transmission. In like fashion, resistor 19!!at photodetector 99 provides a matching function. When an electricaldelay 7' is used, such as in FIGURE 6, coaxial line 101 is a finitelength and is terminated by a resistor 102 of such magnitude that noreflections occur. A movable tap coaxial line 164 is provided to pickoil the wave from line 101 at any one of a number of points. Thisfeature provides an electrical, variable, discretely incre mented delay'7'. When an optical delay is utilized, as in FIGURE 5, then coaxialline M1 is joined directlyrwith line 96.

The signals from lines 96 and 104 (or 101) are summed together and thenapplied to a multiplying circuit comprised of a semiconductor diode 97acting as a square law detector. Diode 97 may be made of silicon, and ithas an extremely fast response time within the frequency range underconsideration (10 1O c.p.s.). The output from the detector 97 is appliedto an amplifier tuned to pass only components having the. beat frequencyw w where these two frequencies are the modulating frequencies of lightchoppers 93 and 98. Amplifier 193 may have a slow response time.

In operation, the output signal from photodetector 94 can be representedby the term I e while that from photodetector 99 is l e Both I and I arecomplex quantities. These signals are first summed (I1e +I2 2 and thensquared by diode 97, so that the resulting signal 12 to amplifier 103 isI e +I e ""2 -+2I I e *2- Since amplifier 1G3 passes only the componenthaving the beat frequency (412-011, the side components of I and I arefiltered out, leaving a signal proportional to the product I 1 Thissignal may then be integrated with respect to time to obtain thecorrelation.

A rigorous analysis of the above-described high speed unit indicatesthat it will provide correct answers when analyzing light beams having anarrow frequency bandwidth (abont kc.), if the modulating frequencie and0.12 are quite low (about 100 c.p.s.). The beat Luz-L01 should also besmall.

An alternative scheme to the optical modulation shown in FIGURE 7 isthat shown in FIGURE 8. No light choppers are used prior to thephotodetectors. Instead, the photocathode is substituted for thethermoelectric emitter surface of a cathode type ray tube, with thecollecting anode serving as a target. Acceleration and focusing voltagesare provided, as Well as a set of deflection plates. A low frequencydeflection signal, either electromagnetic or electrostatic in nature, isthen applied to modulate the magnitude of the signal E at the output ofthe anode. FIGURE 8 shows only one of the photodetectors, however, twoof these are required for the two channels. It is also possible toemploy the mulitplying circuits of FIGURES 7 and 8 when the coherencephase 6 is modulated according to wt.

Concerning the signal to noise S/N ratio of the embodiments shown inFIGURES 5 and 6, an analysis similar to the one made for FIGURE 3 can beperformed. This shows that S/N is proportional to /I I [u (1){ whenusing coherent background, while it is proportional to \/I I [oc (1')|without coherent background. These figures should be compared withEquations 15 and 3, respectively.

As previously mentioned in connection with Equation 17, thecross-spectral density G (V) may be calculated for any V by taking theFourier transform of a (-r). This method involves determining each valueof a (-r) when 1- has a range of 0 to When certain boundary conditionsare established, Equation 17 may be transformed into a series expansionwhich uses discrete values of 'y (1-). Such discrete values of 1- may beeasily obtained by the movable tap delay arrangement shown in FIGURE 6,or by the optical delay arrangement in FIG- URE 5. This simplifiedformula may be derived as follows: From Equation 16, the value of 'y(1-) is since 04 (7) and G (V) are Fourier transform pairs. Now assumethat the highest frequency in G (V) is V Then, G (V) can be representedby the Fourier series +m 61 E izrmvlvo Next inserting Equations 29 and30 into Equation 27, the Fourier transform of (7) is obtained by usingits sampling values; namely where discrete values of 'r=n/v ,(n=0, 1,00) are 13 employed. Thus, when employing the apparatus of FIG- URE orFIGURE 6 for purposes of measuring (7) and its corresponding phase (1-),for use in Equation 31, only certain discrete delays 1- need besupplied. It should be noted, however, that the Equation 31 may only bevalid in the case where the incident light falling on the twophotodetectors is a portion of a uniform plane wave emanating from asource Whose spectrum is to be analyzed. In this case, G ('r) =G11(T),so that essentially an autocorrelation is derived of the intensityfluctuations.

The circuit of FIGURE 9 provides means, through the use of coherentbackground, to measure the value of G (V) directly without need for themathematical calculations shown by Equation 31. The superpositioning ofthe phase shifted (0) coherent beams 134 and 135 upon incident beams 1and 2, respectively is performed by structure as previously shown inFIGURE 6. The currents from photodetectors 117 and 118 are transmittedto tuned amplifiers 119 and 126, respectively, each of which isselectively settable to any frequency w, which is in the spectrum of theincident beams. The outputs from tuned amplifiers 119 and 120 arerespectively mixed with outputs from the local oscillators 122 and 125at mixers 121 and 124. Local oscillator 122 has a frequency of :9 sothat the output signal from mixer 123 has a frequency al -(x2 Likewise,the output from mixer 124 has a frequency Le -m After these signals haverespectively passed through I.F. amplifiers 123 and 125, they aremultiplied together in multiplier 127. This operation results in anoutput signal having a frequency ca -e1 which is then passed through thetuned low frequency amplifier 128 (w w2) to one input of a quartersquare multiplier 131 constructed according to page 281 of theaforementioned book Electronic Analog Computers. The local oscillatorfrequencies ca and 01 are also beat together at mixer 129 to generate asignal having a frequency tel -L0 This signal is applied to a variablephase shifter 130 which shifts its input signal 6:11-1:22 by an angle p.Thereafter, the signal is applied to the other input of multiplier 131.

The output of multiplier 131 is a measurement of the function (w, )e rwhere 09 is defined as the cross-spectral density of intensityfluctuations of the superposed light beams at photodetectors 117 and118. The quantity 4 00,) may be mathematically derived by applying aFourier transformation to the cross-correlation function defined byEquation 22 in accordance with the Wiener-Khintchine theorem in thetheory of stochastic processes. Thus,

In Equation 32 above, the bracketed expression [7129) e i(wo7'+6)]R inthe third term represents its real part. The complete third term ofEquation 28, which is the only one depending on 0, may be reduced to thefollowing:

f man amas(we-wt)= 12 vb 5) where the G function has been expressed interms of 21? times the frequencies involved.

Inserting Equations 33, 34, and 35 into Equation 32,

fvhhere w is the frequency of the coherent background ig t.

As noted previously, the analyzer comprising tuned amplifiers 119, 120,128, mixers 121, 124, 129, local oscilla tors 122, 125, and multipliers127, 131, measure the function (w )e /h if no coherent background werepresent, then the output from motor 131 could berepresented by I (w)eThese above-identified circuits are quite similar to a form of analyzerdeveloped by H. Takahasi and H. Gamo, reported in the Proceedings of theJapan Electrical Communication Engineering Conference, I-28, November1951, and thus do not comprise a part of the present invention. Asimilar form of cross-spectral analyzer is reported by Uberoi andGilbert, in The Review of Scientific Instruments, vol. 30, No. 3, pp.176-180, March 1959. In the multiplier 131, the frequency components ai-m cancel out since they are present at both inputs.

In examining Equation 36, it is noted that a change in angle 0 of thecoherent background will affect only the third term which contains r andei". Therefore any variation in the output of multiplier 131, when only0 is adjusted, can be attributed to a change only in l2( o+ i) 12* et)When the effect of both phases p and 0 is considered, the terms ofinterest become e P[e "G (w -w lf (Er in since the output of multiplier131 is i '(w e P.

The procedure for ascertaining G (w +w and will now be described. Bysetting =0, the output of multiplier 131, as 0 is varied, changesaccording to the change in the real part of Sin the term 12( O+ l)+ 12(O l) of q tion 37 has a phase H then Equation 37 may be expressed asNow, when 0 is varied until H -0==O, then maximum output is obtainedfrom multiplier 131. When 0 is varied until H0=1r, then minimum outputis obtained, such that Next, set PZZQTF/Z so that the term eis reducedto When comparing the integrals of Equation 33 with the generaldefinition of G (V) in Equation 16, it is observed that 1 5 This termmay also be expressed as 12( o+ l) 12( o l)] where the superscript Iindicates the imaginary part only.

Since the term [G (w +m -G (w w has a phase H then Equation 40 may beexpressed as i[ 12( o+ i) 12( o" i)]i sin Now, when is varied until H-0=7r/2, then maximum output is obtained from multiplier 131. When 0 isvaried until H -0=1r/2, then minimum output is obtained, such that M =I12( D+M) 12( o i)l Having the values of Equations 39 and 42, coupledwith the values of H and H (since the values of 6 are known), it is asimple matter to calculate G (w +w and G (w w by the followingequations, in which G represents G (w -w and G represents Gm(w wSubtracting, instead of adding the two equations above, it is seen thatThus, for any set value of w; in tuned amplifiers 119 and 120, thevalues of the complex cross spectrum densities G (w +w and G (w w forthe incident beams 1 and 2 maybe found. Amplifiers 119 and 120 may nowbe tuned to a new o In this way, the entire frequency spectrum of theincident light beams 1 and 2 may be found when using a coherent lightbackground in the circuit of FIGURE 9.

Since the actual value of 0 in FIGURE 9 may be difficult to measure,mirrors 116 and 112, together with photodetector 134 are provided togenerate a signal A(l+ cos wt) which is phase shifted by unit 133 andthen applied to one input of the two-phase motor 132. The other input tomotor 132 is provided from multiplier 131 via amplifier 131', so thatangle 0 is equal to b. Thus, the quantity 1/ may be used, together with.p, for determining the values of G (w +w and G (w -w;). This is thesame technique as utilized in the preceding embodiments.

It may therefore be appreciated that the novel concept embodied inFIGURE 9 is the use of the coherent background beams 134a and 135 whichare respectively superposed upon incident beams 1 and 2 so that completeinformation concerning the cross-spectrum function G (V) may beobtained.

FIGURE 10 shows another embodiment of the crossspectral density analyzerusing coherent background which has less complex electronic circuitry,but which requires at least two difierent interference filters toselectively eliminate either G (w +w or G (w -w from appearing at itsoutput. The optical portion of this embodiment is the same as that shownin FIGURE 9, and so it is not shown in detail in FIGURE 10. Incidentbeams 1 and 2 are respectively superposed on the coherent beams (phaseshifted by 0) at photodetectors 143 and 144. The output currentstherefrom are passed through amplifiers 143 and 144, respectively, whichare selectively tuned at m After multiplication in 145, any change inthe output of amplifier 146 (tuned at to, where e wt) when 0 is variedis due to the sum of l2( o+ i)+ l2( o i) In order to determine each ofthese terms separately, howonly the other remains. This is accomplishedby utilizing an interference filter through which the light beams pass.

The procedure is as follows. Select a filter 140 which prevents thetransmission of incident beam frequencies represented by (m -oTherefore, as phase 9 is varied (or I/ when modulating 0 and usingsynchronous detection), the output varies according to the real part ofG (w +w )e which may be expressed as where on is the phase of G (w.,+wWhen maximum signal output is obtained, then 0:01. The value of !G (w,+w may be derived from the Max-Min 2 equation.

Next select a filter 149 to cancel the term G (w '+w from the output,leaving only G (w w )eto vary according to 6. The complete informationabout G (w w may then be ascertained in a manner explained above. Thus,both G (w +w and G (w w for any set value of m may be found.

While representative embodiments of the invention have been disclosedand described, further modifications may become apparent to thoseskilled in the art without departing from the spirit of the invention asexpressed in the appended claims.

What is claimed is: V

1. Apparatus for the measurement of the phase angle of the phasecoherence factor of first and second beams of coherent light, comprisingin combination: a first photodetector means responsive to said firstlight beam for generating a first output current, a second photodeteotormeans responsive to said second light beam for generating a secondoutput current, correlator means responsive to said first and secondcurrents for producing an output indicative of the cross correlationfunction between sa-id first and second light beams at said photodetectors, an indicator connected to the output of said correlatormeans, said indicator producing an indication of a maximum output ofsaid correlator, a coherent background source of light, meansforproducing first and second equal intensity portions of coherent lightfrom said source, means for respectively superposing said first andsecond portions of said coherent light background on said first andsecond beams at said first and second photodetectors, and means forselectively changing the phase relationship between said first andsecond coherent portions to the phase relationship which produces amaximum correlation output indication, said last-named phaserelationship being indicative of the phase angle of said phase coherencefactor.

2. Apparatus according to claim 1 in which said phase changing meanscomprises means for varying the optical path traveled by one of saidcoherent light portions.

3. Apparatus according to claim 1 in which said phase changing means isperiodically modulated, and which further includes means for generatinga signal corresponding to said modulated phase, means for variably phaseshifting said signal, and synchronous detection means responsive to bothsaid phase shifted signal and said correlator output signal.

4. Apparatus according to claim 3 wherein said synchronous detectionmeans comprises a two phase motor.

5. Apparatus according to claim 3 in which said phase changing meanscomprises means for varying the optical path traveled by one of saidcoherent light portions.

6. Apparatus according to claim 1 in which said correlator includesmeans for generating a signal represent ing the Fourier transformationof said cross correlation function.

7. Apparatus according to claim 6 which further includes interferencefilter means inserted in the paths of said superposed beams forselectively filtering out one sideband of the spectrum of said first andsecond beams.

8. Apparatus for the measurement of the phase angle of the phasecoherence factor of first and second beams of coherent light, comprisingin combination: a first photodetector means responsive to said firstlight beam for generating a first output current, a second photodetectormeans responsive to said second light beam for generating a secondoutput current, first means for selectively changing the phaserelationship between said first and second beams, correlator meansresponsive to said first and second currents for producing an outputindicative of the cross correlation between said first and second lightbeams at said photodetectors, an indicator connected to the output ofsaid correlator means, said indicator pro ducing an indication of amaximum output of said correlator, a coherent background source oflight, means for producing first and second equal intensity portions ofcoherent light from said source, means for respectively superposing saidfirst and second portions of said coherent light background on saidfirst and second beams at said first and second photodetectors, andsecond means for selectively changing the phase relationship betweensaid first and second coherent portions to the phase relationship whichproduces a mam'mum correlation output indication, said last-named phaserelationship being indicative of the phase angle of said phase coherencefactor.

9. Apparatus according to claim 8 in which said first phase changingmeans comprises means for selectively delaying one of said photodetectorcurrents.

10. Apparatus according to claim 8 in which said first phase changingmeans comprises means for selectively varying the optical path traveledby one of said first and second beams.

11. Apparatus according to claim 8 in which said second phase changingmeans comprises means for varying the optical path traveled by one ofsaid coherent light portions.

12. Apparatus according to claim 8 in which said second phase changingmeans is periodically modulated, and which further includes means forgenerating a signal corresponding to said modulated phase, means forvariably phase shifting said signal, and synchronous detector meansresponsive to both said phase shifted signal and said correlator outputsignal.

13. Apparatus according to claim 12 in which said synchronous detectoris a two phase motor.

14. Apparatus according to claim 12 in which said first phase changingmeans comprises means for selectively delaying one of said photodetectorcurrents.

15. Apparatus according to claim 12 in which said first phase changingmeans comprises means for selectively varying the optical path traveledby one of said first and second beams.

16. Apparatus for the measurement of the phase angle of the phasecoherence factor (7) of first and second light beams, where (1')indicates that the coherence time is not zero at first and secondphotodetectors, comprising in combination: a source of coherent light,means for producing first and second equal intensity beams of coherentlight from said source, means for selectively changing the optical pathlength of one of said coherent beams so as to change the phase betweensaid coherent beams, means for respectively superposing said firstcoherent beam on said first light beam at said first photodetector, andfor superposing said second coherent beam on said second light beam atsaid second photodetector, said first and second photodetectorsrespectively producing first and second currents proportional to theintensity of their respective superposed beams, variable time delaymeans, which includes a delay of zero seconds, for selectively delayingone of said currents with respect to the other current, a multiplierresponsive to said one delayed current and said other current, and anintegrator responsive to the output from said multiplier, an indicatorconnected to the output of said multiplier for indicating the particularoptical path length which produces a maximum output from saidintegrator, said last-named optical path length being indicative of thephase angle of said phase coherence factor.

17. Apparatus for the measurement of the cross spectral density G 0) offirst and second light beams at first and second photodetectors, where(v) is the frequency under examination, comprising in combination: asource of coherent light, means for producing first and second equalintensity beams of coherent light from said source, means forselectively changing the optical path length of one of said coherentbeams so as to change the phase between said coherent beams, means forrespectively superposing said first and second coherent beams on saidfirst and second beams at said first and second photodetectors, saidfirst and second photodetectors respectively producing first and secondcurrents proportional to the intensity of their respective superposedbeams, and means responsive to said first and second currents forgenerating the Fourier transform of the cross correlation function ofsaid superposed beams at said first and second photodetectors.

18. Apparatus according to claim 17 which further includes interferencefilter means inserted in the paths of said superposed beams forselectively filtering out one sideband of the spectrum of said first andsecond beams.

19. Apparatus for the measurement of the phase angle of the phasecoherence factor of first and second beams of coherent electromagneticradiations comprising in combination: a first electromagnetic detectormeans responsive to said first beam for generating a first outputcurrent, a second electromagnetic detector means responsive to saidsecond beam for generating a second output current, a correlator meansresponsive to said first and second currents for producing an outputindicative of the cross correlation function between said first andsecond beams at said detectors, an indicator for indicating a maximumoutput from said correlator means, a coherent References Cited in thefile of this patent UNITED STATES PATENTS Strong et a1. Feb. 3, 1953OTHER REFERENCES Twiss et al.: Interferometry of the intensityfluctuations in light 1, Proceedings of The Royal Society of London,vol. 242 A, 1957, pages 300-324.

Twiss et al.: Interferometry of the Intensity of fluctuations in lightII, Proceedings of The Royal Society of London, vol. 243 A, 1958, pages291-319.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No.3,160,696 December 8, 1964 V Hideya Gamo It is hereby certifiedthat'error appears in the above numbered pat- Y ent requiring correctionand that the said Letters Patent should read as corrected below.

Column 3, line 9, for "respectviely" read respectively line 60, strikeoutthe comma, both occurrences; column 4, line 7, for reesultant" readresultant line 67, for "yl2 read --yl2' column 5, line 39, for theright-hand portion of the formula reading:

d 1R rea :IR

column 8 line 23, column 12, lines 31, 33, 39 and 40, for "a",

each occurrence, read y same column 8, line 70', for

"y (r)" read YEEZ'CT) column 11, line 3, for "V read V column 12, line25,. for "mulit l in read multiplying same column 12, Equations 26, 27,28, 30 and 31, the "v", each occurrence, should be in the upper case Vline 73, for =nl" read n=l line 75, for "v read V column 13, lines 42and 45, exponent "1'', each occurrence should be a prime; column 13,line 60, for

6 (W. T'+' read (w 1+6) column 14, line 17 for I l T 'read Q1 lines 32and 35, for "ei each occurrence, read e same lines 32 and 35, for "eeachoccurrence, read esame column 14, lines 49 and 75, for "e'i eachoccurrence, read e lines 49 and 75, for "e each occurrence, read ecolumn 15, line 7, for "(H -e" read (H -e) line 20, for "(m -m firstoccurrence, read (w fluf) same column 15, equations 43 and 44, for "6'",each occurrence, read G Signed and sealed this 18th day of May 1965.

(SEAL) Attest:

ERNEST W. SWIDER EDWARD J. BRENNER Attesting Officer l a Commissioner ofPatents

1. APPARATUS FOR THE MEASUREMENT OF THE PHASE ANGLE OF THE PHASE COHERENCE FACTOR OF FIRST AND SECOND BEAMS OF COHERENT LIGHT, COMPRISING IN COMBINATION: A FIRST PHOTODETECTOR MEANS RESPONSIVE TO SAID FIRST LIGHT BEAM FOR GENERATING A FIRST OUTPUT CURRENT, A SECOND PHOTODETECTOR MEANS RESPONSIVE TO SAID SECOND LIGHT BEAM FOR GENERATING A SECOND OUTPUT CURRENT, CORRELATOR MEANS RESPONSIVE TO SAID FIRST AND SECOND CURRENTS FOR PRODUCING AN OUTPUT INDICATIVE OF THE CROSS CORRELATION FUNCTION BETWEEN SAID FIRST AND SECOND LIGHT BEAMS AT SAID PHOTODETECTORS, AN INDICATOR CONNECTED TO THE OUTPUT OF SAID CORRELATOR MEANS, SAID INDICATOR PRODUCING AN INDICATION OF A MAXIMUM OUTPUT OF SAID CORRELATOR, A COHERENT BACKGROUND SOURCE OF LIGHT, MEANS FOR PRODUCING FIRST AND SECOND EQUAL INTENSITY PORTIONS OFF COHERENT LIGHT FROM SAID SOURCE, MEANS FOR RESPECTIVELY SUPERPOSING SAID FIRST AND SECOND PORTIONS OF SAID COHERENT LIGHT BACKGROUND ON SAID FIRST AND SECOND BEAMS AT SAID FIRST AND SECOND PHOTODETECTORS, AND MEANS FOR SELECTIVELY CHANGING THE PHASE RELATIONSHIP BETWEEN SAID FIRST AND SECOND COHERENT PORTIONS TO THE PHASE RELATIONSHIP WHICH PRODUCES A MAXIMUM CORRELATION OUTPUT INDICATION, SAID LAST-NAMED PHASE RELATIONSHIP BEING INDICATIVE OF THE PHASE ANGLE OF SAID PHASE COHERENCE FACTOR. 